Part IV. Externalities and the Coasian solution. An externality can be corrected
ID: 1160666 • Letter: P
Question
Part IV. Externalities and the Coasian solution. An externality can be corrected via a tax, leading to the efficient allocation. Likewise, two parties could mutually agree to solve the externality even without the intervention of the government. This problem illustrates this using an adaptation of a famous example of externalities, with honey bees and an orchard. The idea is that the bees benefit from the orchard, and the orchard benefits from the bees, so there is a mutual externality. In our example, we will make the benefits flow in only one direction to simplify the algebra. Still, we are doing something different than lecture in the algebra because the externality from the bees will shift the cost function of the orchard. As a result, the external benefits from bees depends on the level of production of the orchard.
Suppose that a beekeeper makes honey, which she sells in a competitive market with equilibrium price P H = 14. The total cost of producing honey is T CH = H2+10H, where H denotes the quantify of honey produced. The beekeeper is located next to an orchard that grows apples that the orchard owner sells on a competitive market at price P A = 17. The total cost of producing apples is T CA = A2 + 10A - HA, where A denotes the quantity of apples. Note that the cost of producing apples depends on the amount of honey. The idea is that more honey requires more bees, and the more bees there are, the easier it is to grow apples. The benefit that bees provide to the orchard is a classic example of an externality.
13. If the beekeeper maximizes her profits, ignoring the externality (i.e., there is no policy and no Coasian bargaining), how many units of honey does she produce, and what are her profits? We will denote this level of honey as Hp . (2 points)
14. Assuming that the beekeeper produces Hp units, which you found in the first part, how many apples will the orchard owner produce, and what will be his profits? (2 points)
15. Now, find the socially optimal level of honey production and apple production. We will denote these as H*and A* . (4 points)
(Hint: You can write total profits as a function of both H and A and take partial derivatives, yielding two equations in 2 unknowns. Or, you can solve for Ap as a function of H, and then substitute this into an expression for total profits—both honey and apple—in the economy, yielding an equation with only one unknown.)
16. The Pigouvian prescription will work just fine in this situation. Suppose that a government intervened in this market by creating a subsidy for honey. What subsidy level would lead to the social optimum allocation? (2 points)
17. The idea behind Coasian bargaining is that private parties could negotiate to get to the private optimum by making some exchange, even without a corrective tax or other policy intervention. What is the maximum amount of money that the orchard owner would be willing to pay to get the beekeeper to change from Hp to H? ? And, what is the minimum amount of money that the beekeeper would be willing to accept to change her production from Hp to H*? (4 points)
By definition, it must be the case that the beekeeper’s profits fall be less than rise in the orchard owner’s profits in moving from the private outcome to the social optimum. This means that the there should be scope for a Pareto improving exchange. That could be achieved under lots of different prices or contracts, but the point in calculating the values above is to show that there is a range of mutually agreeable prices that would cause both people to benefit if they reached a private agreement to increase H. No tax or other policy is needed if it is easy for the two people to make this trade.
Explanation / Answer
Pigouvian taxes are corrective taxes levied on each and every unit of output an externality-generator agent produces. It's named after economist Arthur C. Pigou, who developed the suggestion in his booklet The Economics of Welfare, 1920. Pigouvian taxes are used to be able to scale down the ugly penalties of externalities, peculiarly in incredibly polluting industries.
Take into account the diagram under, which shows the graphical representation of a bad externality concern utilizing a polluting factory as an illustration. The horizontal axis or x-axis measures the quantity of output produced by way of the polluting factory and the vertical axis or the y-axis measures fiscal units. The marginal improvement curve (MB) represents the marginal improvement of the factory for each and every degree of production which declines as the quantity of output raises. The marginal confidential rate curve (MPC) shows the marginal price of the manufacturing unit as output rises. The more the manufacturing facility produces, the more it pollutes and for that reason the higher the uncomfortable side effects, which is represented through the marginal injury curve (MD). Ultimately, the marginal social fee (MSC) represents the total marginal rate for the whole society, and is constructed by way of adding together the exclusive expenses (which immediately translate to bigger prices) and social expenses.
On this scenario, we've got a poor externality equal to E, and the equilibrium is set at an output degree of QA at a rate PA. A Pigouvian tax could be imposed, with a purpose to eliminate such terrible externality. This tax would decrease the output produced to QS, and develop fee to PS, being this a socially efficient equilibrium. Purchaser surplus decreases A+C+F, whilst producer surplus decreases with the aid of subject B+D+G. Government will gain a tax revenue equal to subject A+B+C+D, drawn in mild pink in the diagram. In the end, external marketers will gain E+F+G. Consequently, the online effect is E:
-(A+C+F)-(B+D+G)+(A+B+C+D)+(E+F+G)=E
The unintended effects of the externality are for that reason eliminated utilizing a Pigouvian tax. Nevertheless, a critique can quite simply be made: it looks like Pigouvian taxes shrink the willingness to supply. Indeed, the cautious implementation of Pigouvian taxes require them to be imposed on the polluting side of the manufacturing unit, instead than immediately impose them on output stages. Most likely, it may be really rough to surely make this big difference.